Into the sad scene steps one of the city’s most senior statesmen — the dean of its congressional delegation, in fact — seizing the spotlight all to himself, accusing the NYPD of racism, and besmirching his city once again.

And, of course, causing that much more unnecessary agony, confusion and doubt for the family of the slain hero.

Such is the special talent of Rep. Charlie Rangel, who remains so deeply mired in the past that he cannot trudge beyond the old race battles that were the foundation of his career — decades ago.

How much it must confuse the old political dinosaur to know that President Obama wouldn’t occupy the White House today if it were not for his genuine commitment to leaving those old wars in the past and his steadfast refusal to play the game of racial politics — no matter how much it might help him personally in any given situation.

And because Obama passed through that eye of the needle, so did America.

Left on the other side, unable to get through, are the clanging screamers for whom it’s always been about nothing more than shameless self-promotion.

But, it turns out, even the all-powerful Democratic chairman of the House Ways and Means Committee can’t make “off-the-cuff” jokes about the president getting shot.

It was “entirely inappropriate to bring the president and his wife into this discussion,” Rangel says now, two days later.

As apologies go, it was a lame one. What about trying to whip up racial hatred out of thin air, Charlie? What about the department and the city you maligned? What about the families most directly involved?

Still, for Rangel, it was huge.

Remember, this is a guy who never backs down, who only attacks his attackers, who never admits wrongdoing — no matter how corrupt or how much of your money is lost in the deal.

So, the reigning question is: Why?

Certainly not because it was in anyone’s best interest other than his own. That’s simply not how the man operates.

Not because people were offended.

People are always offended by Rangel’s tax-cheating, nest-lining, profligate ways.

No matter what Rangel says, somebody, someplace high up got to him and told him to back off.

Asked about it yesterday, the White House did not flatly deny involvement.

Nor did they simply dismiss the question by saying they would never join Rangel in the cow pies he manages to wallow in every few months or so.

Instead, the White House simply declined to comment. The silence was deafening.